Why is the speed of light in a vacuum constant? Why does light never travel faster or slower than 299 792 458 m / s? By Dilip D James M.A., A(mus) T.C.L
This seemingly innocuous question is both extremely interesting and extremely important, not least because it is a question that has never been answered. Why is the speed of light constant? It is a question that has never been answered, at least not by Einstein, he did not have an answer as to why the speed of light was constant he merely postulated that the speed of light in a vacuum is constant. The fact that this question as to the constancy of the speed of light in a vacuum has never been adequately explained is deeply disturbing.
Our whole conception of the Universe and of the space-time continuum is based on the constancy of the speed of light in a vacuum, yet we have absolutely no explanation for why this is so. Our understanding of gravity also depends on the constancy of the speed of light, since the whole of General Relativity is based on this singular fact. Exploring further, why is the speed of light constant only in a vacuum? Surely, this is an equally disturbing circumstance? If the speed of light in a vacuum is constant doesn’t it follow that the speed of light in any medium should also be constant? And it is! The difficulty lies in the fact that the speed of light in a medium other than water can be exceeded. The speed of light travelling in water can be exceeded ny fast electrons in Cherenkov radiation. Why? Logically, if Einstein is right when he states that that light is the limiting speed of the Universe, it shouldn’t happen. One of the reasons that the postulate of the constancy of the speed of light has been accepted is that it serves to demonstrate mass-energy equivalence. This seems reasonable, especially when given substance by the invention of nuclear weapons and nuclear energy. However, what if there were an alternate reason for mass-energy equivalence? What if the reason for mass-energy equivalence is not connected in any way to the speed of light being constant but merely exists as the result of some alternative reason? In stating this consider the fact that the problem of mass-energy equivalence had been a major idea for a long time. J. J. Thomson the discoverer of the electron had dabbled with the idea as had Oliver Heaviside. Poincare was the first to use the equation E = mc² although he did not specifically state that mass and energy are interchangeable. These investigations arose from the fact that it was known that when matter radiated energy ( electromagnetic radiation) a loss of mass resulted. Therefore, it stood to reason that the radiated energy carried away some of the mass. Consider the following sentence very, very carefully, for it is the way in which the mass-energy equivalence was first written. “If a body gives off the energy L in the form of radiation, its mass diminishes by L/V².” This was the form that mass-energy equivalence originally took, not as an equation but as a written sentence. Einstein used V to mean the speed of light in a vacuum and L to mean the energy lost by a body in the form of radiation. Since the speed of all electromagnetic radiation is constant and has been very accurately measured to be 299 792 458 m / s it follows that in the equation given above V² can be replaced by c² . Thus here the term c² has a real meaning and in the equation e = mc² c is equal to 299 792 458 x 299 792 458 m / s = 8.98755179 × 10¹⁶ m² / s² Thus when we speak of the energy in a kilogram of matter to be equal to 8.98755179 × 10¹⁶ J we mean exactly that and mathematically it is very satisfying.
The problem of matter-energy equivalence has been at the centre of attention of physicists for quite a long time before Einstein came up with the equation e = mc2. In hindsight it is not difficult to see why this was so. The newly discovered radio-waves (electromagnetic radiation) made by Hertz, gave rise to many unanswered questions. What were these radio waves? How were these radio waves able to convey energy, heat etc., Obviously if anything can convey energy it must possess momentum, yet these radio waves had no mass! Hence the equation for momentum p = mv could not apply. How was it possible for an object to convey energy without possessing mass? In the same way the equation for potential energy was p.e = mg was also ruled out since gravity cannot act on an object with zero mass. When Einstein came up with his equation for the energy of a photon it seemed to offer a solution to the problem of matter-energy equivalence. While other physicists and mathematicians might have got bogged down in the intricacies of trying to correlate magnetic and electric fields into their equations: Oliver Heaviside coming up with m = (4⁄3) E / c^2 where E is the energy of a spherical electric field and Poincare got E = 3/4 mc^2 in which he tries to indicate the increase in mass of a moving electron. Einstein who had only very recently come up with his equation for photon energy, thought in terms of light being more particle than wave, probably came up with the simpler version of the equation which he later proved through experimental work to be correct. If you take the kinetic equation KE = mv^2/2 , and substitute v with c (the speed of light) the equation becomes KE = mc2^/2, since the photon is never at rest and possesses zero rest mass this can translate to simply E = mc^2.
Another way of looking at the problem is to take the relations between energy, force and momentum:
E = distance through which force acts , since distance can be approximated to c.
E = force x c
And
Momentum gained = force x time during which force acts: time can be equated with c
This means that: Force = m x c
If both equations are put together then e = force x c = (m x c) x c = E = mc²
Another way of looking at the problem is to take the two relations between energy, force and momentum:
E = distance through which force acts , since distance can be approximated to c
E = force x c
And
Momentum gained = force x time during which force acts: time can be equated with c
This means that: Force = m x c
If both equations are put together then e = force x c = (m x c) x c = E = mc²
One solution using calculus is:
When a body moves at a speed close to the speed of light, a force F acts on it and, as a result, the energy E of the body increases. Since the speed of the body v cannot exceed c and, as the force continues to act, the speed v approaches c . We have:
In this last equation, t is the independent variable. So the equation tracks how energy E(t), mass m(t) and speed v(t) grown as a function of time t.
In order to determine how mass increases as the energy of the body increases, it is necessary to make energy E the independent variable; and to take time t(E), mass m(E) and speed v(E) all to be functions of E. Multiplying the last equation by:
and using the chain rule, gives:
Taking the limit in which the energy E grows large. In that limit, v approaches c and:
approaches zero. In this limit:
The result is this equation. It says that mass m grows incrementally by 1/c²
for each unit of energy E added. While this result holds generally, this simple demonstration returns the result only in the special case in which the energy E of the body has grown so large that its speed is close to c. These calculations are not so important as the fact that they yielded extremely accurate results, so much so, that experiments eventually resulted in the development of the atomic bomb and nuclear power.
Returning now, to the question of why the speed of light is constant. Classical physicists had known for a long time that the speed of a wave in a medium is independent of the speed of either the source or of the observer. The speed of a wave (and it has been proved beyond any doubt by innumerable experiments) in a medium is governed solely by the properties of the medium. Increasing the energy imparted to the wave will not affect its speed in any way, it will stay the same although the amplitude (i.e., its up and down motion) of the wave might increase. When the medium changes so does the speed of the wave, but within that medium, its speed will remain constant, this is exactly how light behaves also. Similarly, waves follow the inverse square law of dispersion meaning that the intensity of the wave reduces by the square of the distance, light also behaves in the same way. I fact taken all together the wave description of light completely and exactly fulfills all of the properties of light. Both Special Relativity and General Relativity fall dismally short of doing so.
We have now come full circle and have returned to the original idea that there must be a medium through which light propagates. This premise explains every possible attribute of light including the manner and speed at which it propagates, its dispersion according to the inverse square law and its behaviour as both particle and wave. For those who would like to read more about this theory. Please read my paper on the Electromagnetic Universe at Academia:
